Solve for $x$ : $ 7|x + 6| + 10 = 1|x + 6| + 2 $
Answer: Subtract $ {1|x + 6|} $ from both sides: $ \begin{eqnarray} 7|x + 6| + 10 &=& 1|x + 6| + 2 \\ \\ { - 1|x + 6|} && { - 1|x + 6|} \\ \\ 6|x + 6| + 10 &=& 2 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 6|x + 6| + 10 &=& 2 \\ \\ { - 10} &=& { - 10} \\ \\ 6|x + 6| &=& -8 \end{eqnarray} $ Divide both sides by ${6}$ $ \dfrac{6|x + 6|} {{6}} = \dfrac{-8} {{6}} $ Simplify: $ |x + 6| = -\dfrac{4}{3}$ The absolute value cannot be negative. Therefore, there is no solution.